Cats and lions come from the same ancient family of animals called Felidae, which lived millions of years ago. Over time, this family split into different groups, and each group adapted to its surroundings. One group became big cats like lions, who live in open areas and hunt in groups. Another group became smaller cats, like the domestic cats we have today, which live close to people. Even though they ended up different, they still have a lot in common, like their sharp claws, similar body shapes, and hunting habits.
Everyone shares the same ancestors if you go back far enough! For cats and lions, you’d need to go back about 30 million years to when the first Felidae species evolved. These first cats were the common ancestors of both lions, house cats, and every other Felid species (big cats, bobcats, lynxes, and so on).
Whenever DNA makes a copy of itself, sometimes mistakes are made that alter the genetic code. Most of these are harmless, some are dangerous, and a very few are actually helpful. For example, let’s say it’s 30 million years ago and there’s a lot of cats on the scene. The animals they hunt have learned to look out for these large predators and to hide in dense vegetation. One of these cats randomly acquires a mutation that makes it a little smaller. Now, it can navigate through that vegetation AND it needs less energy to stay alive, which means less hunting required. Something like this may have lead to the evolution of smaller cat species.
There’s benefits to being large, too, though. It keeps you at the top of the food chain and means you’re able to take down larger prey, so some populations of early cats would have evolved to get bigger and bigger. These are just hypotheticals, but the point is that all life comes from a single common ancestor, and that random changes happen over time in individuals. Very very rarely, one of these changes will be beneficial and lead to that organism having more babies that survive to adulthood. But that doesn’t mean that the other organisms in that species who don’t have the mutation just disappear. That’s how new species can emerge from one common source.
You and your siblings are a little different. You and your siblings together are different from your first cousins. You’re even more different from your second cousins. Times that by a few million. The nearest common ancestor of domestic cats and lions was several million years ago. Small differences add up over time.
All living organisms undergo minor mutations over time.
Natural selection dictates that organisms with beneficial mutations survive and are able to reproduce, giving these mutations to their offspring. Organisms without these mutations fall victim to what is called selection pressures. For example, a selection pressure for an evolving giraffe could be eating leaves from tall trees. A long neck allows these giraffes to feed, while those without that specific mutation would starve.
Same basic premise across the entirety of evolution. Lions and cats (I assume you mean domestic house cats) share the same single celled ancestor as every other species, and they fall into the same category because there’s not as much difference between them as, say, a spider and a whale.
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